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A thin cylinder of 100 mm internal diameter and 5 mm thickness is subjected to an internal pressure of 10 MPa and a torque of 2000 Nm. Calculate the magnitudes of the principal stresses (in MPa)

A
109.8, 45.2
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B
109.8, 40.2
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C
109.8, 31
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D
109.8, 50
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Solution

The correct option is B 109.8, 40.2
Given :
Di = 100 mm,
Do = 110 mm,
D=105 mm

For Thin cylinder

J=πDt(D24)=π×105×5×(52.5)2

=4547729mm4=4.547×106mm4

τmax=T×rmaxJ

where
rmax=Do2=55mm

τmax=2000×103×554.547×106=24.20MPa

σH=σc=pdi2t=100MPa

σL=50MPa


σ1σ2=1502±252+24.202

=75±34.8=109.8,40.2MPa

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